Mobility of Ions in LiquidHe4I andHe3as a Function of Pressure and Temperature

Abstract

In this paper we present an experimental study of the pressure and temperature dependence of the mobility of the positive and negative species of charged particles in liquid ${\mathrm{He}}^{4}$ above the $\ensuremath{\lambda}$ transition and in liquid ${\mathrm{He}}^{3}$. The mobility of the positive species in ${\mathrm{He}}^{4}$ decreases linearly with increasing density, and the Stokes radius of the positive species is inversely proportional to ${T}^{\frac{1}{2}}$. The mobility of the negative species initially increases with increasing density and then falls off linearly with further increase in density. The Stokes radius of the negative species increases with increasing temperature. At constant density the mobilities of both species in ${\mathrm{He}}^{4}$ and ${\mathrm{He}}^{3}$ vary very slowly with temperature. At the vapor pressure and around 2.2\ifmmode^\circ\else\textdegree\fi{}K there is a larger temperature dependence than indicated above, but this is probably due to the approach of the $\ensuremath{\lambda}$ transition. The mobility of the positive species in ${\mathrm{He}}^{4}$ and ${\mathrm{He}}^{3}$ at 3.0\ifmmode^\circ\else\textdegree\fi{}K is a linear function of density, independent of the isotope.Feynman has suggested (and Kuper detailed) a model for the negative species in which an electron is trapped in a bubble of radius $b$. Comparison with our data shows that this model is not able to account for the temperature and pressure dependence of the observed mobility. In the Appendix, we show that an electron would not diffuse by quantum mechanical tunneling from cavity to cavity.Davis, Rice, and Meyer have derived an expression for the mobility of the negative species by assuming (a) that the negative species is a free electron and (b) that scattering is determined by a small pseudopotential equal to the polarization potential outside an atom and zero inside the atom. They predict a mobility which initially increases with increasing density at constant temperature, but they cannot predict the decrease of mobility with further increase in density unless they assume a density dependent effective mass of the electron. The effective mass necessary to fit theory to experiment is approximately 100 electron masses and is proportional to the square of the density. This model is promising, but more detailed calculations of the effective mass must be made before the mechanism of negative charge transport may be considered to be completely understood.